If you're talking about the 300D, then you probably do have a liquid to liquid heat exchanger in the bottom of the radiator to cool the transmission fluid (my '85 300TD does, and so do most cars nowadays), and it seems likely that you need to get that fixed and probably have your trans serviced ASAP.

The radiator should come right out the top once you have undone the shroud (and flopped it back over the fan), the top radiator mounts, and the many large and small hoses -- the small ones at the bottom will gush some ATF, so if you're planning to reuse your coolant because it's fresh, get that all drained and the pan out of the way before you undo the ATF hoses.

My older son also has a '91 318i, but with 215,000 miles -- I've got to do a clutch on that one at Christmas time.